The weak separation condition was introduced by Lau and Ngai in [1]}; this definition is not the original but equivalent by [2]}.
Standard arguments show that any IFS satisfying the \(\Phi \) -FNC necessarily satisfies the weak separation condition (see, for example, [3]}, [4]}).
Moreover, when \(K\)  is a convex set, the weak separation condition implies that the \(\Phi \) -FNC holds with respect to the iteration rule \(\Phi \)  from ex:weighted-transition [3]}.
